In this paper, we introduce the concept of isotropic Hilbert-valued spherical random field, thus extending the notion of isotropic spherical random field to an infinite-dimensional setting. We then establish a spectral representation theorem and a functional Schoenberg’s theorem. Following some key results established for the real-valued case, we prove consistency and quantitative central limit theorem for the sample power spectrum operators in the high-frequency regime.

Asymptotics for isotropic Hilbert-valued spherical random fields / Caponera, Alessia. - In: BERNOULLI. - ISSN 1350-7265. - 30:3(2024), pp. 1723-1745. [10.3150/23-BEJ1650]

Asymptotics for isotropic Hilbert-valued spherical random fields

Alessia Caponera
2024

Abstract

In this paper, we introduce the concept of isotropic Hilbert-valued spherical random field, thus extending the notion of isotropic spherical random field to an infinite-dimensional setting. We then establish a spectral representation theorem and a functional Schoenberg’s theorem. Following some key results established for the real-valued case, we prove consistency and quantitative central limit theorem for the sample power spectrum operators in the high-frequency regime.
2024
High-frequency asymptotics, ‎Hilbert spaces, isotropy, Quantitative Central Limit Theorem, ‎spectral representation, Spherical random fields.
Asymptotics for isotropic Hilbert-valued spherical random fields / Caponera, Alessia. - In: BERNOULLI. - ISSN 1350-7265. - 30:3(2024), pp. 1723-1745. [10.3150/23-BEJ1650]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11385/244733
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